Question

A new city Mayor would like to determine if community members are paying less for gas prices in his city this year compared to last year. He surveys 16 random community members and conducts hypothesis test about the mean cost of gas prices, which was 2.45 dollars last year, using a 5% significance level. Determine the critical value(s) using the partial t-table above. If entering two critical values, use ±

Answer 1

Answer: $\pm1.753$

Step-by-step explanation:

Let $\mu$ be the population mean and  $\mu_0$ be the actual mean price.

By considering the given information, we have

$H_0: \mu=\mu_0\\\\H_a:\mu<\mu_0$

Given : Sample size : n= 16, which is a small sample so the test applied here is t-test.

Significance level : $\alpha=0.05$

Degree of freedom =$df=n-1=16-1=15$

By using the standard normal distribution t-table, the critical value for t-test will be :-

$t_{(df, \alpha)}=t_{(15,0.05)}=\pm1.753$

Hence, the  the critical value will be $\pm1.753$